No, Jesus didn't cut Himself off from the world; it's just that inwardly He was disconnected all the time. Not in a daze, not distant, but always concentrating on the spiritual life within Him. We surely need to practice that with diligence.
Jesus wasn't a religious nut and we shouldn't be, either. He was so ordinary that the religious leaders of the day called Him a glutton and wine drinker! That doesn't mean for you to go run out to an all-you-can-eat buffet then have a beer! Rather, let the Spirit of God manifest its robust holiness through you. The disconnect from the world is not external but internal; in that way you will learn to be interested only in what God is interested in and can easily wade through the muck down here on the journey to your eternal home.
Proverbs 3:5-6, "Trust in the Lord with all your heart, and do not lean on your own understanding. In all your ways acknowledge Him and He will direct your path". Endure the fire…it's producing pure gold!